Feed: Dr. Myron Evans
Posted on: Sunday, January 16, 2011 6:39 AM
Author: metric345
Subject: Paul Dirac’s Original Thinking
| This thinking was described by Paul Dirac to John B. Hart as in Kerry’s biography, with a photogaph of Dirac during a conference organized by Hart. It was based on Clifford algebra. For a change, there is a good wikipedia article on the Dirac equation as originally formulated. In my opinion negative energy and the Dirac sea is a non starter, and as the wiki article shows, was actually rejected by Dirac and contemporaries in the thirties. The chiral rep is the correct one to use, it eliminates negative energy, so I have been using it for some years. As can be seen on the foot of page 2 of the wiki article it was thought originally that one could use E = c root (p squared + (mc) squared) of the Einstein equation and use the usual quantum mechanical operator equivalents for E and p, expand in a series and iterate to a solution. Clearly, the negative root of E was never considered as meaningful, and it obviously is not, because negative energy or electron cascade have never been observed. Essentially, what Dirac did was to factorize the d’alembertian in terms of the 4 x 4 Dirac matrices in standard rep. That meant automatically that the wavefunction must be a column vector with four entries, all four of which pertain to the fermion. The Dirac matrices in chiral rep are different, but nonetheless give all that the standard rep gives, but without the artificial problem of negative energy. The Dirac matrices in standard rep are given in the wiki article on page 4. In my books and articles they are given in the modern chiral rep. I also derived the Dirac equation from geometry, but a more powerful one – Cartan geometry. I realized that thr Dirac spinor can be rearranged into a 2 x 2 matrix from a 1 x 4 column vector, and vice versa. The 2 x 2 matrix is a tetrad in SU(2) rep space. As described in page 8 of the wiki article the Dirac sea has been replaced by the Bogoliubov transformation and from the forties onwards by the method of QED (albeit to me, AND Feynman himself, very unsatisfactory). About a year or more ago I discovered (UFT 129 and 130) that the Dirac equation can be written as one chiral rep equation in 2 x 2 matrices in which negative energy is not a problem. I intend to develop this in UFT 172 giving complete details. Some of these have already been posted as notes for UFT 171. Chemists are taught the Dirac equation very vaguely as L + 2S and that’s that.
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